Here are the essential concepts you must grasp in order to answer the question correctly.
Inverse Functions
Inverse functions are pairs of functions that 'undo' each other. If f(x) is a function, its inverse, denoted as f⁻¹(x), satisfies the condition f(f⁻¹(x)) = x for all x in the domain of f. This means that applying the function and then its inverse returns the original input.
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Graphing Logarithmic Functions
Composition of Functions
The composition of functions involves combining two functions to form a new function. For two functions f and g, the composition is denoted as (f ∘ g)(x) = f(g(x)). To verify if f and g are inverses, we need to check if both f(g(x)) = x and g(f(x)) = x hold true for all x in their respective domains.
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Linear Functions
Linear functions are functions of the form f(x) = mx + b, where m is the slope and b is the y-intercept. They graph as straight lines and have constant rates of change. Understanding the properties of linear functions is essential when determining their inverses, as the inverse of a linear function is also linear, provided the slope is not zero.
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